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Mathematica Algebra Wolfram Language

Could you please help me out to get equations from augmented matrix

Muzahoo jee

Posted 10 years ago

Hi, I am trying to derive equations from an augmented matrix, but i'm not been able to, could anyone please help me out to convert these printed equations into real algebraic equations. Regards. Clear[a, b, c, d, e]; For[j = 1, j <= 5, j++, a = RandomInteger[{-5, 5}, {5, 6}]; b = a[[1 ;; 5, 1 ;; 5]]; c = Table[Subscript["x", i], {i, 1, 5}]; d = b.c; e = \!\(\SubscriptBox[\(a\), \(\(\[LeftDoubleBracket]\)\(All, 6\)\(\[RightDoubleBracket]\)\)]\); For[i = 1, i <= 5, i++, Print[ \!\(\SubscriptBox[\(d\), \(\(\[LeftDoubleBracket]\)\(i\)\(\ \[RightDoubleBracket]\)\)]\), " = ", \!\(\SubscriptBox[\(e\), \(\(\[LeftDoubleBracket]\)\(i\)\(\ \[RightDoubleBracket]\)\)]\)];] Print[" "];] the notebook file is also attached. Attachments:*

Hi, I am trying to derive equations from an augmented matrix, but i'm not been able to, could anyone please help me out to convert these printed equations into real algebraic equations. Regards.

Clear[a, b, c, d, e];
For[j = 1, j <= 5, j++,
 a = RandomInteger[{-5, 5}, {5, 6}];
 b = a[[1 ;; 5, 1 ;; 5]];
 c = Table[Subscript["x", i], {i, 1, 5}];
 d = b.c;
 e = 
\!\(\*SubscriptBox[\(a\), \(\(\[LeftDoubleBracket]\)\(All, 
   6\)\(\[RightDoubleBracket]\)\)]\);
 For[i = 1, i <= 5, i++,
   Print[
\!\(\*SubscriptBox[\(d\), \(\(\[LeftDoubleBracket]\)\(i\)\(\
\[RightDoubleBracket]\)\)]\), " = ", 
\!\(\*SubscriptBox[\(e\), \(\(\[LeftDoubleBracket]\)\(i\)\(\
\[RightDoubleBracket]\)\)]\)];]
  Print[" "];]

the notebook file is also attached.

POSTED BY: Muzahoo jee

4 Replies

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Muzahoo jee

Posted 10 years ago

that is really good regards

POSTED BY: Muzahoo jee

Muzahoo jee

Posted 10 years ago

That is a great help, Regards

POSTED BY: Muzahoo jee

Eric Johnstone

Eric Johnstone, McGill University

Posted 10 years ago

I was curious to see if I could get Muzahoo jee's subscripted form. Combining his and Daniel Lichtblau's code, I came up with this: Table[a = RandomInteger[{-5, 5}, {5, 6}]; b = a[[1 ;; 5, 1 ;; 5]]; c = Table[Subscript[x, i], {i, 1, 5}]; d = b.c; e = a[[All, 6]]; Thread[d == e], {j, 5}] Hey, for me that's a big deal! Cheers, Eric

POSTED BY: Eric Johnstone

Daniel Lichtblau

Daniel Lichtblau, Wolfram Research

Posted 10 years ago

Use `Table` to actually create and return a list rather than simply print it. Table[ a = RandomInteger[{-5, 5}, {5, 6}]; b = a[[1 ;; 5, 1 ;; 5]]; c = Array[x, 5]; d = b.c; e = a[[All, 6]]; Thread[d == e], {j, 5}] (* Out[10]= {{5 x[1] - 2 x[2] - 3 x[3] - 4 x[4] - 4 x[5] == -2, x[2] + 3 x[3] - 4 x[5] == -4, -2 x[1] + 5 x[2] - 4 x[3] - 3 x[5] == 1, 2 x[1] - 4 x[2] - 3 x[3] + 3 x[4] == -4, -3 x[1] - x[3] + 3 x[4] - 4 x[5] == 3}, {x[1] + 4 x[2] - 4 x[3] + 5 x[4] + 2 x[5] == 4, -5 x[1] + x[3] + 3 x[5] == 2, -x[1] - 2 x[2] + 5 x[3] - 3 x[4] + x[5] == -5, -2 x[1] + 4 x[2] - x[3] - 5 x[4] + 3 x[5] == -4, 5 x[1] + 2 x[2] - x[4] + 4 x[5] == 1}, {-x[1] - 4 x[2] + 3 x[3] + 2 x[4] - 4 x[5] == -4, -5 x[1] - 5 x[2] - 3 x[3] + x[4] - 3 x[5] == -3, -x[2] + 3 x[3] + 5 x[4] == 1, -4 x[1] - 3 x[3] - x[4] + 2 x[5] == -1, -5 x[1] + x[2] + 2 x[3] + 5 x[4] + x[5] == -5}, {x[1] + 5 x[2] + 2 x[3] - 4 x[4] == 3, 2 x[1] - 5 x[2] + 4 x[3] - 4 x[4] + 3 x[5] == -4, -3 x[1] + x[2] - 4 x[3] - 4 x[4] - 4 x[5] == -5, x[1] - 5 x[2] + x[3] - 3 x[4] - 2 x[5] == 0, x[1] - x[2] - 2 x[4] - x[5] == 0}, {2 x[1] - 4 x[2] + 5 x[3] - 2 x[4] - x[5] == 1, -x[1] + 2 x[2] - 5 x[3] - 4 x[4] - x[5] == 2, -x[1] + x[2] - 3 x[3] - 3 x[5] == 5, 3 x[1] - 5 x[2] + 5 x[3] + x[4] - 5 x[5] == -5, -3 x[1] + x[2] + 2 x[3] + 5 x[4] - 3 x[5] == -3}} *)

Use Table to actually create and return a list rather than simply print it.

Table[
 a = RandomInteger[{-5, 5}, {5, 6}];
 b = a[[1 ;; 5, 1 ;; 5]];
 c = Array[x, 5];
 d = b.c;
 e = a[[All, 6]];
 Thread[d == e], {j, 5}]

(* Out[10]= {{5 x[1] - 2 x[2] - 3 x[3] - 4 x[4] - 4 x[5] == -2, 
  x[2] + 3 x[3] - 4 x[5] == -4, -2 x[1] + 5 x[2] - 4 x[3] - 3 x[5] == 
   1, 2 x[1] - 4 x[2] - 3 x[3] + 3 x[4] == -4, -3 x[1] - x[3] + 
    3 x[4] - 4 x[5] == 
   3}, {x[1] + 4 x[2] - 4 x[3] + 5 x[4] + 2 x[5] == 
   4, -5 x[1] + x[3] + 3 x[5] == 
   2, -x[1] - 2 x[2] + 5 x[3] - 3 x[4] + x[5] == -5, -2 x[1] + 
    4 x[2] - x[3] - 5 x[4] + 3 x[5] == -4, 
  5 x[1] + 2 x[2] - x[4] + 4 x[5] == 
   1}, {-x[1] - 4 x[2] + 3 x[3] + 2 x[4] - 4 x[5] == -4, -5 x[1] - 
    5 x[2] - 3 x[3] + x[4] - 3 x[5] == -3, -x[2] + 3 x[3] + 5 x[4] == 
   1, -4 x[1] - 3 x[3] - x[4] + 2 x[5] == -1, -5 x[1] + x[2] + 
    2 x[3] + 5 x[4] + x[5] == -5}, {x[1] + 5 x[2] + 2 x[3] - 4 x[4] ==
    3, 2 x[1] - 5 x[2] + 4 x[3] - 4 x[4] + 3 x[5] == -4, -3 x[1] + 
    x[2] - 4 x[3] - 4 x[4] - 4 x[5] == -5, 
  x[1] - 5 x[2] + x[3] - 3 x[4] - 2 x[5] == 0, 
  x[1] - x[2] - 2 x[4] - x[5] == 
   0}, {2 x[1] - 4 x[2] + 5 x[3] - 2 x[4] - x[5] == 
   1, -x[1] + 2 x[2] - 5 x[3] - 4 x[4] - x[5] == 
   2, -x[1] + x[2] - 3 x[3] - 3 x[5] == 5, 
  3 x[1] - 5 x[2] + 5 x[3] + x[4] - 5 x[5] == -5, -3 x[1] + x[2] + 
    2 x[3] + 5 x[4] - 3 x[5] == -3}} *)

POSTED BY: Daniel Lichtblau

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